n+5=4/5*n

Solution for n+5=4/5*n equation:

n+5=4/5n

We move all terms to the left:

n+5-(4/5n)=0


Domain of the equation: 5n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

n-(+4/5n)+5=0

We get rid of parentheses

n-4/5n+5=0

We multiply all the terms by the denominator


n*5n+5*5n-4=0

Wy multiply elements

5n^2+25n-4=0

a = 5; b = 25; c = -4;
Δ = b2-4ac
Δ = 252-4·5·(-4)
Δ = 705
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-\sqrt{705}}{2*5}=\frac{-25-\sqrt{705}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{705}}{2*5}=\frac{-25+\sqrt{705}}{10}
$